Numbers' & Numeral
systems' history and curiosities (2)

The
Mayas, as well as the Aztecs, used a vigesimal (20) numeration.
They developed 3 sets of different graphical notations
to represent numbers: a) with strokes and dots, b) anthropomorphic
figures, c) symbols.

a) The
Mayan base-20 numeral system

b) The
figures shown below indicate numbers from 0 to 10

Chinese
Numbers

The
Peculiarity of the Chinese Numeral Notation

The
Chinese use three numeral systems: the Hindu-Arabic
numerals, along with two indigenous numeral systems,
one for everyday writing (simple numerals), and another
one for use in commercial or financial contexts (complex
numerals). These last ones are used on checks and other
transaction forms because they are much more difficult
to alter. Actually, they are the equivalent of writing
'one', 'two', 'three', etc., rather than 1, 2, 3...

In
the chart below, the first column features European or
Hindu-Arabic numerals; the second one, the standard Chinese
equivalent (simple numerals); and the third column, the "capital" Chinese
characters (complex numerals).

The
Chineses also had several other ways to represent numbers.
The strange geometric figures shown below indicate the
numbers 1 through 10. This numeration style - named shang
fang da zhuan - is still used in official seals.

'Horus
eye' or udjat was
used to transcribe unit measures of capacity for grains,
as you can see below each part of the eye represents
a value in binary unit fraction (fig. 1). The Egyptians
were also the inventors of the
fraction bar. The numerator 1 and the bar were represented
by a graphical symbol suggesting an open mouth; they
used to note the denominators of the fraction under
this symbol (fig. 2). More
info about Egyptian fractions here.

Did
you know that the Romans too could transcribe unit fractions?
E.g. to record1/2
they used the letter S (semis). Knowing that,
what represents SIX?Obviously
not 6, but 8.5 (=10-1-0.5)!

Numbers
1 through 10 in Various Writing Systems(More
numerals in many different writing systems from Omniglot)

Indo-European
Heritage

The
number names in most European languages take their origin
from the Indo-European language. Although various numeration
systems have been used (duodecimal, vigesimal and sexagesimal
numerations), the decimal system survived all of them.
However, we can find traces of the vigesimal system in
some French, Danish and Basque number names.

"Numeral
and Numbers' history and curiosites" are excerpts of our
math columns "Alchimaths". You can read them in the review
'Tangente' (French version). To subscribe write to:Editions Archimède, 5 rue Grandel,
95100 Argenteuil, France

You
are encouraged to expand and/or improve this article. Send
your comments, feedback or suggestions to Gianni
A. Sarcone. Thanks!